1 Answer
1

Both methods should thus give you the same result. The diffusion equation for heat can be derived from Fourier's law.

For a one-dimensional problem, you can do that easily yourself, by taking a inifinitesimal part of the rod of size $dx$ and realizing that $q_x$ at either side of this part should be the same (since there is no heat source or sink in this piece). Taking the limit for $dx \rightarrow 0$, will give you the diffusion equation. If your problem becomes more complex, the diffusion equation will be easier to solve.